Questions: Use the given information to prove that triangle DEF is congruent to triangle DGF. Given: line segment EF is congruent to line segment GF line segment DE is congruent to line segment DG Prove: triangle DEF is congruent to triangle DGF Statement - Reason 1 - line segment EF is congruent to line segment GF - Given 2 - line segment DE is congruent to line segment DG - Given 3 - line segment DF is congruent to line segment DF - Reason?

Use the given information to prove that triangle DEF is congruent to triangle DGF.

Given: line segment EF is congruent to line segment GF

line segment DE is congruent to line segment DG

Prove: triangle DEF is congruent to triangle DGF

Statement - Reason

1 - line segment EF is congruent to line segment GF - Given

2 - line segment DE is congruent to line segment DG - Given

3 - line segment DF is congruent to line segment DF - Reason?
Transcript text: Use the given information to prove that $\triangle D E F \cong \triangle D \dot{G F}$. Given: $\overline{E F} \cong \overline{G F}$ \[ \overline{D E} \cong \overline{D G} \] Prove: $\triangle D E F \cong \triangle D G F$ \begin{tabular}{|lll|} \hline Statement & Reason \\ \hline 1 & $\overline{E F} \cong \overline{G F}$ & Given \\ \hline 2 & $\overline{D E} \cong \overline{D G}$ & Given \\ \hline 3 & $\overline{D F} \cong \overline{D F}$ & Reason? \\ \hline 4 & & \\ \hline \end{tabular}
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Solution

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Solution Steps

Step 1: Identify the given information

We are given that $\overline{EF} \cong \overline{GF}$ and $\overline{DE} \cong \overline{DG}$.

Step 2: Identify the common side

We can see that segment $\overline{DF}$ is a common side to both triangles $\triangle DEF$ and $\triangle DGF$.

Step 3: Apply the SSS congruence postulate

Since we have three pairs of congruent sides: $\overline{EF} \cong \overline{GF}$, $\overline{DE} \cong \overline{DG}$, and $\overline{DF} \cong \overline{DF}$ (reflexive property), we can conclude that the triangles are congruent by the Side-Side-Side (SSS) postulate.

Final Answer

\begin{tabular}{|l|l|} \hline Statement & Reason \\ \hline 1. $\overline{EF} \cong \overline{GF}$ & Given \\ \hline 2. $\overline{DE} \cong \overline{DG}$ & Given \\ \hline 3. $\overline{DF} \cong \overline{DF}$ & Reflexive Property of Congruence \\ \hline 4. $\triangle DEF \cong \triangle DGF$ & SSS Congruence Postulate \\ \hline \end{tabular}

\\(\boxed{\triangle DEF \cong \triangle DGF}\\)

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